Abstract

Parametric subharmonic oscillators and amplifiers at optical frequencies have recently been proposed, using optical maser pump sources together with the nonlinear optical properties of certain crystals. The simplest such structure would comprise a Fabry-Perot resonator filled with nonlinear crystal, the ends being transparent at the fundamental or pump frequency ω and reflecting at the subharmonic frequency ω/2. This paper demonstrates that such a structure will also function as an ideal optical power limiter at the fundamental. Power transmission through the structure at ω will limit sharply and flatly at the threshold level at which subharmonic oscillations commence; a large power-dependent reflection will also occur on the input end above threshold. The use of such a limiter for eliminating spiking in optical masers, and for other purposes, is suggested.

© 1962 Optical Society of America

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References

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  1. W. H. Louisell, Coupled Mode and Parametric Electronics (Wiley and Sons, Inc., New York, 1960).
  2. R. H. Kingston, Proc. IRE 50, 472 (1962).
  3. M. Bass, P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Letters 8, 18 (1962).
    [CrossRef]
  4. P. A. Franken et al., Phys. Rev. Letters 7, 118 (1961).
    [CrossRef]
  5. J. A. Giordmaine, Phys. Rev. Letters 8, 19 (1962).
    [CrossRef]
  6. B. Lax, J. G. Mavroides, D. F. Edwards, Phys. Rev. Letters 8, 166 (1962).
    [CrossRef]
  7. P. D. Maker et al., Phys. Rev. Letters 8, 21 (1961).
    [CrossRef]
  8. A. E. Siegman, Proc. IRE 47, 447 (1959).
  9. I. T. Ho, A. E. Siegman, IRE Trans. on Microwave Theory Tech. MTT-9, 459 (1961).
    [CrossRef]
  10. R. W. DeGrasse, J. Appl. Phys. 30, 155(S) (1959).
    [CrossRef]
  11. F. R. Arams, M. Grace, S. Okwit, Proc. IRE 49, 1308 (1962).
    [CrossRef]
  12. K. L. Kotzebue, J. Appl. Phys.33, to be published (1962).
    [CrossRef]

1962 (5)

J. A. Giordmaine, Phys. Rev. Letters 8, 19 (1962).
[CrossRef]

B. Lax, J. G. Mavroides, D. F. Edwards, Phys. Rev. Letters 8, 166 (1962).
[CrossRef]

R. H. Kingston, Proc. IRE 50, 472 (1962).

M. Bass, P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Letters 8, 18 (1962).
[CrossRef]

F. R. Arams, M. Grace, S. Okwit, Proc. IRE 49, 1308 (1962).
[CrossRef]

1961 (3)

P. A. Franken et al., Phys. Rev. Letters 7, 118 (1961).
[CrossRef]

I. T. Ho, A. E. Siegman, IRE Trans. on Microwave Theory Tech. MTT-9, 459 (1961).
[CrossRef]

P. D. Maker et al., Phys. Rev. Letters 8, 21 (1961).
[CrossRef]

1959 (2)

A. E. Siegman, Proc. IRE 47, 447 (1959).

R. W. DeGrasse, J. Appl. Phys. 30, 155(S) (1959).
[CrossRef]

Arams, F. R.

F. R. Arams, M. Grace, S. Okwit, Proc. IRE 49, 1308 (1962).
[CrossRef]

Bass, M.

M. Bass, P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Letters 8, 18 (1962).
[CrossRef]

DeGrasse, R. W.

R. W. DeGrasse, J. Appl. Phys. 30, 155(S) (1959).
[CrossRef]

Edwards, D. F.

B. Lax, J. G. Mavroides, D. F. Edwards, Phys. Rev. Letters 8, 166 (1962).
[CrossRef]

Franken, P. A.

M. Bass, P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Letters 8, 18 (1962).
[CrossRef]

P. A. Franken et al., Phys. Rev. Letters 7, 118 (1961).
[CrossRef]

Giordmaine, J. A.

J. A. Giordmaine, Phys. Rev. Letters 8, 19 (1962).
[CrossRef]

Grace, M.

F. R. Arams, M. Grace, S. Okwit, Proc. IRE 49, 1308 (1962).
[CrossRef]

Hill, A. E.

M. Bass, P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Letters 8, 18 (1962).
[CrossRef]

Ho, I. T.

I. T. Ho, A. E. Siegman, IRE Trans. on Microwave Theory Tech. MTT-9, 459 (1961).
[CrossRef]

Kingston, R. H.

R. H. Kingston, Proc. IRE 50, 472 (1962).

Kotzebue, K. L.

K. L. Kotzebue, J. Appl. Phys.33, to be published (1962).
[CrossRef]

Lax, B.

B. Lax, J. G. Mavroides, D. F. Edwards, Phys. Rev. Letters 8, 166 (1962).
[CrossRef]

Louisell, W. H.

W. H. Louisell, Coupled Mode and Parametric Electronics (Wiley and Sons, Inc., New York, 1960).

Maker, P. D.

P. D. Maker et al., Phys. Rev. Letters 8, 21 (1961).
[CrossRef]

Mavroides, J. G.

B. Lax, J. G. Mavroides, D. F. Edwards, Phys. Rev. Letters 8, 166 (1962).
[CrossRef]

Okwit, S.

F. R. Arams, M. Grace, S. Okwit, Proc. IRE 49, 1308 (1962).
[CrossRef]

Peters, C. W.

M. Bass, P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Letters 8, 18 (1962).
[CrossRef]

Siegman, A. E.

I. T. Ho, A. E. Siegman, IRE Trans. on Microwave Theory Tech. MTT-9, 459 (1961).
[CrossRef]

A. E. Siegman, Proc. IRE 47, 447 (1959).

Weinreich, G.

M. Bass, P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Letters 8, 18 (1962).
[CrossRef]

IRE Trans. on Microwave Theory Tech. (1)

I. T. Ho, A. E. Siegman, IRE Trans. on Microwave Theory Tech. MTT-9, 459 (1961).
[CrossRef]

J. Appl. Phys. (1)

R. W. DeGrasse, J. Appl. Phys. 30, 155(S) (1959).
[CrossRef]

Phys. Rev. Letters (5)

M. Bass, P. A. Franken, A. E. Hill, C. W. Peters, G. Weinreich, Phys. Rev. Letters 8, 18 (1962).
[CrossRef]

P. A. Franken et al., Phys. Rev. Letters 7, 118 (1961).
[CrossRef]

J. A. Giordmaine, Phys. Rev. Letters 8, 19 (1962).
[CrossRef]

B. Lax, J. G. Mavroides, D. F. Edwards, Phys. Rev. Letters 8, 166 (1962).
[CrossRef]

P. D. Maker et al., Phys. Rev. Letters 8, 21 (1961).
[CrossRef]

Proc. IRE (3)

A. E. Siegman, Proc. IRE 47, 447 (1959).

F. R. Arams, M. Grace, S. Okwit, Proc. IRE 49, 1308 (1962).
[CrossRef]

R. H. Kingston, Proc. IRE 50, 472 (1962).

Other (2)

W. H. Louisell, Coupled Mode and Parametric Electronics (Wiley and Sons, Inc., New York, 1960).

K. L. Kotzebue, J. Appl. Phys.33, to be published (1962).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(a) Simple parametric amplifier and/or subharmonic oscillator. (b) Possible optical version of the same device.

Fig. 2
Fig. 2

The same parametric device operated as an ideal parametric limiter.

Fig. 3
Fig. 3

Analytical model of the optical parametric limiter. The waves are assumed to be uniform plane waves. The various phase angles are added to simplify the analysis—using them, all of the amplitudes E i can be taken real and positive.

Fig. 4
Fig. 4

Spatial variation of the various ω wave amplitudes in the limiter for two different input levels E0 and E0 both above threshold.

Fig. 5
Fig. 5

Division of the input power (~E02) into transmitted, reflected, and subharmonic power above the limiting threshold.

Fig. 6
Fig. 6

Possible method for eliminating “spiking” in optical masers by using an optical limiter.

Equations (28)

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2 E ( z , t ) z 2 μ 2 E ( z , t ) t 2 = μ 2 P t 2 .
| 2 E i z 2 | | ω μ E i z | | ω 2 μ E i 2 | .
d E 1 / d z = κ E + 2 , d E 2 / d z = κ E 2 , d E + / d z = κ E 1 E + * , d E / d z = κ E 2 E * ,
κ = π λ E a
E 3 = E 1 = E 0 , E 4 = E 2 = E + = E = 0.
E 3 = E 1 ( L ) = E 1 ( 0 ) κ E + 2 L = E 0 κ E + 2 L , E 4 = E 2 ( 0 ) = κ E 2 L = κ E + 2 L .
E 0 2 E 3 2 E 4 2 = 2 ( 1 R ) E + 2 = E 0 2 ( E 0 κ E + 2 L ) 2 ( κ E + 2 L ) 2
E + 2 = 1 κ L ( E 0 1 R κ L ) ·
E 3 = E 0 κ L E + 2 = 1 R κ L .
E 0 ( threshold ) = 1 R κ L = 1 R ( π L / λ ) E at .
Input power Threshold power = [ E 0 E 0 ( threshold ) ] 2 = P in P th .
Reflected power Threshold power = [ E 4 E 0 ( threshold ) ] 2 = [ ( P in / P th ) 1 2 1 ] 2 .
Subharmonic power Threshold power = 2 ( 1 R ) E + 2 E 0 ( threshold ) 2 = 2 [ ( P in / P th ) 1 2 1 1 2 ] .
d E + d z = κ [ E 0 ( E 0 1 R κ L ) z L ] E + , d E d z = κ [ ( E 0 1 R κ L ) L z L ] E .
E + ( L ) = E + ( 0 ) exp [ 1 2 κ E 0 L + 1 2 ( 1 R ) ] , E ( 0 ) = E ( L ) exp [ 1 2 κ E 0 L + 1 2 ( 1 R ) ] .
R exp ( 1 R ) R [ 1 + ( 1 R ) ] = 1 ( 1 R ) 2 .
1 2 κ E 0 L = 1 2 ( 1 R ) E 0 E 0 ( threshold ) 1
P in P th 4 ( 1 R ) 2 .
P th = E 0 2 ( threshold ) 2 Z 0 = ( 1 R ) 2 ( π L / λ ) 2 E at 2 2 Z 0 ,
E at = 10 11 V / m 1 R = 10 3 , L = 1 cm , λ = 1 μ .
P th 10 4 W / m 2 = 1 W / cm 2 .
d E + d z = κ E 1 E + .
E + ( z ) = E + ( 0 ) exp [ κ E 1 z ] .
E + ( t ) = E + ( 0 ) exp [ κ E 1 L 2 t T ] · R t / 2 T .
R t / 2 T exp [ ( 1 R ) t 2 T ]
κ E 1 L 2 t T = ( P in P th ) 1 2 ( 1 R ) t 2 T .
P + ( t ) P + ( 0 ) = [ E + ( t ) E + ( 0 ) ] 2 = exp { [ ( P in P th ) 1 2 1 ] ( 1 R ) t T } .
t b = T ( 1 R ) [ ( P in / P th ) 1 2 1 ] ln [ P + ( s s ) P + ( 0 ) ] .

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